Sure, let's solve this step by step:

Step 1: Let's denote the side of the equilateral triangle as 'a'.

Step 2: The area of the equilateral triangle is given by the formula: Area = √3/4 * a²

Step 3: The diameter of the circle is equal to the side of the equilateral triangle, which is 'a'. Therefore, the radius of the circle is a/2.

Step 4: The area of the circle is given by the formula: Area = π * (a/2)² = π/4 * a²

Step 5: Now, we need to find the ratio of the area of the circle to the area of the triangle. This is given by (π/4 * a²) / (√3/4 * a²)

Step 6: Simplifying this, we get the ratio as π / √3.

So, the ratio of the area of the circle to the area of the equilateral triangle is π / √3.

Question

Sure, let's solve this step by step:

Step 1: Let's denote the side of the equilateral triangle as 'a'.

Step 2: The area of the equilateral triangle is given by the formula: Area = √3/4 * a²

Step 3: The diameter of the circle is equal to the side of the equilateral triangle, which is 'a'. Therefore, the radius of the circle is a/2.

Step 4: The area of the circle is given by the formula: Area = π * (a/2)² = π/4 * a²

Step 5: Now, we need to find the ratio of the area of the circle to the area of the triangle. This is given by (π/4 * a²) / (√3/4 * a²)

Step 6: Simplifying this, we get the ratio as π / √3.

So, the ratio of the area of the circle to the area of the equilateral triangle is π / √3.

Knowee AI · Accepted Answer